Late drama at Kingspan Stadium tonight saw the lead change hands twice in the last five minutes as Paddy Jackson's drop goal two minutes from time cancelled out Gareth Steenson's effort to edge the slenderest of victories for Ulster over Exeter Chiefs.
Ulster bagged the only try of the game through Sean Reidy after stellar work from man-of-the-match Charles Piutau, but the high standard of kicking from Belfast native Steenson on his old stomping ground kept the Chiefs in touch throughout the clash - and the out-half was desperately unlucky not to snatch a victory in the dying seconds with another drop that veered just wide.
Ulster sit third in Pool Five with four points on the back of the victory, a point behind Bordeaux-Bègles who picked up a late bonus point in Clermont, while Exeter now face a mammoth task to progress to the knock-out stages, sitting bottom on a single losing bonus point from tonight's game.
Piutau, Kyle McCall, Pete Browne and Roger Wilson all returned to the starting lineup for the Chiefs' visit, with Piutau on the left wing the only change to the backline which had started against Bordeaux-Bègles. The New Zealander was joined by Jared Payne at full-back, captain Andrew Trimble on the other flank, Luke Marshall and Stuart Olding in the centre, and the half-back pairing of Jackson and Ruan Pienaar.
McCall made up a bulky front row with Rory Best and Rodney Ah You, supported by locks Browne and Franco van der Merwe, and a back row of Iain Henderson and Reidy either side of Wilson.
Flashes of individual brilliance from Piutau lit up an otherwise lacklustre first half where try-scoring opportunities were in scant supply and well-drilled defence from both sides was the order of the day.
Both teams had plenty to prove after poor Round One showings, and Ulster made all the running straight from the off, Jackson slotting an early penalty after a neat combination between Payne and Browne.
Steenson equalised within moments, and while Ulster enjoyed a good spell of pressure with first an abortive attempt from van der Merwe and two menacing rolling mauls, the killer punch was lacking and Chiefs eventually cleared their lines on 18 minutes.
Exeter made no better use of their subsequent period of possession until the ever-reliable Steenson kicked over his second just before the half-hour mark - at which point Ulster exploded into life. Piutau was the architect with a jinking run through the heart of the Chiefs defence, Reidy finishing off the move with a smart sidestep of his own to elude the last man.
Jackson converted and it wasn't long before Piutau was off again, slaloming past three would-be tacklers to make good ground towards half-way, then sliding in to make a try-saving interception metres from his own line once possession had been surrendered and Chiefs had spotted a gap.
Half-Time Score Ulster 10 Exeter Chiefs 6
A late tackle on Piutau minutes after the restart got Ulster a five-metre rolling maul which Exeter defended stoutly, but a great aerial take by Trimble as Chiefs cleared their lines kept play just in the visiting half, from where Jackson coolly slotted a penalty on 49 minutes.
However poor concentration at the restart allowed Julian Salvi to pick up the ball unchallenged in the Ulster '22', setting up a chain of events which culminated in a simple kick in front of the posts for Steenson.
Jackson missed the chance to re-extend the lead to seven on 63 minutes with a wayward penalty, and soon it was cut to a single point as Steenson once again split the posts from close range.
Quick hands from Olding, Marshall and Pienaar were instrumental in the next attack, drawing the infringement on the '22', from where Jackson's kick was never in doubt. However, neither was Steenson's fifth on 73 minutes, as replacement Rob Herring - playing in the back row - was pinged right in front of the posts for failing to roll away in the tackle.
Exeter pressed high, Steenson biding his time until the opportunity presented itself - and when it did on 76 minutes, the out-half dropped the goal with plenty of time to spare to put his side 18 - 16 to the good.
With the clock running down, Ulster wasted no time in pouring down the other end of the pitch, crafting out the opportunity for Jackson to do just the same.
90 seconds remained for the final Exeter chance, and when it came once again in the form of a Steenson drop goal, KIngspan Stadium held its breath as the kick drifted agonisingly inches wide of the right-hand upright.
Full-Time Score Ulster 19 Exeter Chiefs 18
Ulster (15 - 9) Jared Payne; Andrew Trimble (c), Luke Marshall, Stuart Olding, Charles Piutau; Paddy Jackson, Ruan Pienaar
(1 - 8) Kyle McCall, Rory Best, Rodney Ah You, Pete Browne, Franco van der Merwe, Iain Henderson, Sean Reidy, Roger Wilson
Replacements (16 - 23) Rob Herring, Andy Warwick, Ross Kane, Alan O'Connor, Clive Ross, Paul Marshall, Craig Gilroy, Tommy Bowe
Exeter Chiefs (15 - 9) Lachlan Turner; Olly Woodburn, Ian Whitten, Henry Slade, James Short; Gareth Steenson (c), Dave Lewis
(1 - 8) Moray Low, Jack Yeandle, Harry Williams, Mitch Lees, Geoff Parling, Kai Horstmann, Julian Salvi, Tom Waldrom
Replacements (16 - 23) Elvis Taione, Carl Rimmer, Tom Francis, Jonny Hill, Dave Dennis, Jack Maunder, Sam Hill, Ollie Devoto